Question

Prove that log(1 + 2 + 3) = log 1 + log 2 + log 3. Is it true for any three numbers
m, n, p?​

Answer 1

GIVEN:

• Log(1 + 2 + 3) = log 1 + log 2 + log 3.

TO PROVE:

• Log(1 + 2 + 3) = log 1 + log 2 + log 3.

EXPLANATION:

•°• Log(1 + 2 + 3) = log 1 + log 2 + log 3

★ Log a + Log b = Log(ab)

•°• Log(1 + 2 + 3) = log (1 × 2 × 3)

•°• Log(6) = log (6)

Hence proved.

TO CHECK:

• Is log(m + n + p) = log m + log n + log p true for any three numbers.

EXPLANATON:

°•° log(m + n + p) = log m + log n + log p

★ Log a + Log b = Log(ab)

°•° Log(m + n + p) = log (m × n × p)

°•° Log(m + n + p) = log (mnp)

Cancel log on both sides.

°•° m + n + p = mnp

So this true only for numbers whose sum and product are equal.